Method and apparatus for measuring surface topography

ABSTRACT

A method for measuring surface topography characterized by making multiple scans of the surface with a laser scanning unit and utilizing the multiple scans to create representations of the surface&#39;s topography. The surface topography data can also be used to calculate the compressive or tensile stress caused by a thin film applied to the surface of a semiconductor wafer. The apparatus of the present invention scans a laser beam across a surface in an x direction, and detects displacements of a reflected portion of the laser beam in a z direction. A pair of photodetectors are used to translate z direction displacements of the reflected beam into analog signals which are digitized and input into a microcomputer for analysis. The multiple scans of the surface are preferably accomplished by placing the workpiece on a pedestal which can be rotated to various angular positions.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a continuation of prior application Ser. No. 08/317,115 filed onOct. 3, 1994, now U.S. Pat. No. 5,532,499, which is a divisionalapplication of Ser. No. 08/225,425 filed on Apr. 8, 1994, now U.S. Pat.No. 5,369,286, which is a continuation of application U.S. Ser. No.08/144,141, filed Oct. 27, 1993, now abandoned, which is a divisional ofapplication U.S. Ser. No. 07/876,576, filed Apr. 30, 1992, now U.S. Pat.No. 5,270,560, which is a continuation-in-part of application U.S. Ser.No. 07/822,910, filed Jan. 21, 1992, now U.S. Pat. No. 5,233,201, whichis a continuation-in-part of U.S. Ser. No. 07/357,403, filed May 26,1989, now U.S. Pat. No. 5,118,955 all applications being commonlyassigned herewith, the disclosures of which are hereby incorporated byreference herein in their entirety.

BACKGROUND OF THE INVENTION

This invention relates generally to methods and apparatus for measuringsurface topographies and more particularly to methods and apparatus formeasuring the surface topographies of semiconductor wafers, hard diskplatters, optical blanks and other high-tolerance workpieces.

Integrated circuits are formed on semiconductor wafer substrates by anumber of processing steps. These steps include deposition, etching,implantation, doping, and other semiconductor processing steps wellknown to those skilled in the art.

Thin films are typically formed on wafer surfaces by a depositionprocess. These thin films can comprise, for example, silicon dioxide,AlSi, Ti, TiN, PECVD Oxide, PECVD Oxynitride, doped glasses, silicides,etc. The thickness of such films usually ranges from about a few hundredangstroms to several micrometers. Often, three or more film layers areformed on the surface of a single semiconductor wafer.

In the art of fabricating semiconductor wafers, it is of knownimportance to minimize or control stresses in surface films. Highsurface stresses can cause, for example, silicide lifting, the formationof voids or crack and other conditions that adversely affectsemiconductor devices (i.e. chips) which are fabricated on the wafers.In practice, surface stresses become more problematical as the level ofcircuit integration increases, and are especially troublesome whenfabricating large scale integration (LSI), very large scale integration(VLSI), and ultra large scale integration (ULSI) semiconductor devices.

The stress in the surface film of a semiconductor wafer can be eithercompressive or tensile. A compressive stress in a surface film willcause a wafer to slightly bow in a convex direction, while a tensilestress in a surface film will cause a wafer to slightly bow in a concavedirection. Therefore, both compressive and tensile stresses cause thesurface of the semiconductor wafer to deviate from exact planarity. Theextent of the deviation from planarity can be expressed in terms of theradius of curvature of a wafer surface. In general, the greater themagnitude of surface stress, the smaller the radius of curvature.

Because of the problems that can be caused by stresses in surface filmson semiconductor wafers, it is highly desirable to be able to measuresuch stresses. The measurements can be used, for example, to identifywafers that are likely to provide low yields of semiconductor devices orwhich might produce devices prone to early failure. In normal practice,stresses in surface films are not measured directly but, instead, areinferred from measurements of the radius of curvature of the surface ofinterest.

A system for measuring film stress by measuring the radius of curvatureof a wafer is described in an article entitled "Thermal Stresses andCracking Resistance of Dielectric Films on Si Substrates," A. K. Sinhaet. al., Journal of Applied Physics, Vol. 49, pp. 2423-2426, 1978. Othersystems are described in copending patent applications Ser. No.07/822,910, filed Jan. 21, 1992 and U.S. Ser. No. 07/357,403, filed May26, 1989. All of these systems linearly scan across a wafer to determinethe curvature of the wafer along that scan line. This type of waferscanning can be referred to as a "1-D" linear scan reflecting the factthat it is a one-dimensional scan of the wafer's surface, such as in thex direction. A 1-D scan is quite effective for wafers having fairlyuniform surface topographies and uniform film layers, but may be lessthan adequate for more complex surface topographies or for film layersthat are somewhat uneven. This is because the radius of curvature forsuch wafers may be significantly different when taken along differentscan lines along the surface of the wafer. If the particular scan linechosen provides a radius of curvature is which far from the averageradius of curvature, the film stress calculated from the radius ofcurvature will be incorrect.

There are other applications for a method and apparatus for measuringsurface curvature besides determining the mechanical stress in films.For example, it is often deskable to know the surface curvature (i.e.the "flatness") of hard disk platters or the radius of curvature ofoptical elements. In the prior art, such curvature measurements weremade by expensive laser interferometry equipment.

SUMMARY OF THE INVENTION

A method for measuring the topography of a surface in accordance withthe present invention involves scanning a laser beam across the surfacealong a first scan line, detecting a reflected portion of the beam todevelop first scan data, scanning the laser beam across a second scanline which intersect the first scan line at a predetermined angle,detecting a reflected portion of the beam to develop second scan data,and utilizing the first scan data and the second scan data to representthe topography of the surface. Preferably, second scan of the wafer isaccomplished by rotating either the scanning mechanism or the surface bya predetermined angle φ=360/Ns degrees, where Ns is the number of scansof the surface.

In a preferred embodiment, the first scan line and the second scan lineare aligned at a reference point. This can be accomplished by choosingan arbitrary reference point on a curve derived from data from the firstscan, and aligning a corresponding point on a curve derived from datafrom the second scan with the reference point. The multiple scans can beused to provide a three dimensional representation of the curvature ofthe surface, or a two dimensional contour map of the surface.

A further method in accordance with the present invention involvesscanning a surface of a workpiece prior to the deposition of a film toobtain blank displacement data and then scanning the surface of theworkpiece after film deposition to obtain deposited displacement data.These two sets of data are subtracted to eliminate the effects of theintrinsic curvature of the surface. Preferably, multiple scans are madeboth before and after film deposition to provide the aforementionedadvantages of multiple scanning.

An apparatus of the present invention includes a scanning unit and adata processing unit. The scanning unit has a diode laser which can scana beam spot across the surface of a workpiece in an x direction. A beamdetector detects z direction displacements of a reflected portion of thelaser beam caused by the surface curvature of the workpiece and outputsa signal representative of that displacement. This signal is digitizedand can be analyzed to determine surface curvature, contours, and filmstress.

The beam detector utilizes a pair of adjacent photodetectors which, whencombined with the detector circuitry of the present invention, providean output which indicates the relative position of the reflected beamspot.

An advantage of the present invention is that multiple scans of theworkpiece surface provides a better understanding of the topography ofthe wafer surface and also provides a better estimate of the stressinherent in a film applied to the surface of a semiconductor wafer.

These and other advantages of the present invention will become apparentto those skilled in the art upon a reading of the followingspecification of the invention and a study of the several figures of thedrawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial view of an apparatus for measuring surfacetopography in accordance with the present invention;

FIG. 2 is a pictorial view of the scanning mechanism of the scanningunit illustrated in FIG. 1;

FIG. 3 is a schematic of the beam detector, bus driver, and businterface of the present invention;

FIG. 4 is a pictorial view of the beam detector, a beam spot, and agraph depicting the output Q of the circuit of FIG. 3;

FIG. 5 is a block diagram of a method for measuring surface topographyin accordance with the present invention;

FIG. 5a is a block diagram of the input parameter step 88 of FIG. 5;

FIG. 5b is a block diagram of the calibrate beam detector step 92 ofFIG. 5;

FIG. 5c is a block diagram of the obtain blank wafer data step 94 ofFIG. 5;

FIG. 5d is a block diagram of the obtain deposited wafer data step 100of FIG. 5;

FIG. 5e is a block diagram of the process data step 102 of FIG. 5;

FIG. 5f is a block diagram of the align multiple curves step 176 of FIG.5e;

FIG. 6 is a graph illustrating various system outputs for one scanacross a wafer surface;

FIG. 7 is a graph illustrating six surface curvatures taken from sixscans across a wafer surface;

FIG. 8 is used to further illustrate the align multiple curves step 176of FIGS. 5e and 5f;

FIG. 9 illustrates the output data step 104 of FIG. 5 wherein themultiple scans of the wafer surface are used to display athree-dimensional representation of the curvature of the wafer surface;and

FIG. 10 illustrates the output data step 104 of FIG. 5 wherein themultiple scans of the wafer surface are used to display atwo-dimensional contour map of the wafer surface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In FIG. 1, a surface topography measuring apparatus 10 includes ascanning unit 12 and a data processing unit 14. The scanning unit 12includes an enclosure 16 having a front access or opening 18, and arotatable pedestal 20 accessible through the opening 18. A workpiece,such as a wafer 22, rests on pedestal 20. While the present inventionwill be discussed in terms of measuring the curvature of a semiconductorwafer, such as wafer 22, it should be understood that this invention canbe used to non-destructively measure the surface topography of a varietyof workpieces, including hard disk platters, optical blanks, etc. Asused herein, "topography" refers to any description of a surface of aworkpiece, such as curvature, contours, etc.

Data processing unit 14 preferably comprises a commercially availablepersonal computer, such as an IBM-PC AT class personal computer orequivalent. A data bus 24 couples the scanning unit 12 to the dataprocessing unit 14. Preferably, the data processing unit 14 has anappropriate I/O card with A/D converters plugged into one of itsexpansion slots such that analog data produced by scanning unit 12 onbus 24 can be converted into digital data for the data processing unit14. Alternatively, scanning unit 12 can provide digital data on bus 24,which can enter data processing unit 14 through an existing digital I/Oport such as an RS-232C serial port. Appropriate control busses may alsoconnect data processing unit 14 to the scanning unit 12 in a manner wellknown to those skilled in the art.

FIG. 2 illustrates a portion of the scanning mechanism 26 housed withinthe enclosure 16 of FIG. 1. The mechanism 26 includes a diode laser 28,a beam directing assembly 30, a beam detector 32, a z stage assembly 34,an x stage assembly 36, and a pedestal assembly 38 including theaforementioned pedestal 20.

Diode laser 28 is preferably a Class IIIb laser product certified by theFederal Food and Drug Administration under FDA 27 CFR 1040, 10(f)(5)(ii)and preferably operates at a wavelength of approximately 780 nm. Atypical maximum power output of the laser 28 is less than 2mW.

The beam directing assembly 30 includes a converging lens 40 and a frontsilvered mirror 42. The converging lens 40 should have a focal lengthwhich allows a beam B produced by laser 28 to form a beam spot on thewafer surface s of about 3 mm in diameter and a beam spot on thedetector 32 which is approximately 20-50 μm in diameter. The laser 28forms an incident beam Bi which impinges upon the surface of the wafer22. The surface s of the wafer 22 reflects a portion of the incidentbeam Bi as a reflected beam Br. The reflected beam Br impinges upon thereflective surface of mirror 42 and is reflected towards the beamdetector 32 as a directed beam Bd. Therefore, beam B comprises the sumof beams Bi, Br, and Bd. The effective reflected beam path lengthcomprising beam Br and Bd is about 300 mm.

The beam detector 32 preferably includes a photodetector assembly whichwill be described in greater detail subsequently. The beam detector 32is responsive to the position along a z axis of the beam spot developedby beam Bd and is operative to produce an electrical signalrepresentative of the z position. The z Stage assembly 34 includes a zstage 46 including a nut 48 engaged with a lead screw 50. The lead screw50 is driven by a shaft 52 of a stepper motor 54. Rotation of the shaft52 causes the z stage 46 and, therefore, the beam detector 32 totranslate upwardly or downwardly in a direction parallel to the z axis.The stepper motor 54 has the characteristic that it can be operated tomove stage 46 in discrete, reproducible increments. In practice, suchincrements result in advancing or retracting the stage 46 in the zdirection in increments of about 0.6 microns.

The x stage assembly 36 includes an x stage 56 which supports the diodelaser 28, the beam directing assembly 30, the beam detector 32, and thez stage assembly 34. The x stage assembly 36 also includes a nut 58coupled to the x stage 56, a lead screw 60 engaged with the nut 58, anda stepper motor 62 having a shaft 64 coupled to the lead screw 60.Again, the lead screw and stepper motor are conventional and permit thestage 56 to be moved incrementally along the x axis. In practice, suchincrements result in advancing or retracting the stage 56 in incrementaldistances of about 0.025 mm.

The pedestal assembly 38 includes the aforementioned pedestal 20, whichis preferably disk shaped and has a diameter somewhat larger than thediameter of the wafer 22 (or other workpiece) that it is intended tosupport. The pedestal 20 is, itself, supported by a drive reductionmechanism 66 coupled to the shaft of a stepper motor 68. The steppermotor 68 is operative rotate pedestal 20 and wafer 22 around an axisparallel to the z axis. In other words, the wafer 22 is caused to rotateparallel to or in the x-y plane, where the y axis extendsperpendicularly to the plane of the paper. The incremental angle φ ofrotation of the pedestal 20 is preferably given by the equation:

    φ=360/Ns                                               (equation one)

where Ns is the number of scans across the upper surface s of the wafer22. The rotational resolution of the stage is typically in the range of0.1 to 0.01 degrees.

In FIG. 3, the beam detector 32 includes a first photodetector A and asecond photodetector B. Photodetectors A and B can be conventionaldevices such as silicon PIN diodes. Photodetectors A and B aresubstantially rectangular in configuration and abut along one of theirlonger sides along a line 70. Photodetector A develops an electricaloutput signal on a line 72 which is related to the energy of theelectromagnetic radiation impinging upon its surface, and photodetectorB develops an electrical output signal on a line 74 which is related tothe energy of the electromagnetic radiation impinging upon its surface.More specifically, the electrical output signals on lines 72 and 74 areanalog signals having amplitudes which vary with the intensity of thebeam Bd, its frequency, and the size of the spot which the beam Bdprojects onto the beam detector 32.

FIG. 3 also shows a bus driver 76 which drives data bus 24 and acomputer interface circuit 78. The bus driver 76 includes adifferential-voltage operational amplifier 80 and a summing amplifier82. In practice, both operational amplifier 80 and summing amplifier 82are conventional integrated operational amplifier devices, where thesumming amplifier is embodied as an operational amplifier with aninverter at its negative input terminal. Line 72 is coupled to thepositive input terminal of operational amplifier 80 and to one of thepositive input terminals of summing amplifier 82. Line 74 is coupled tothe negative input terminal of operational amplifier 80 and to apositive input terminal of summing amplifier 82. The outputs ofoperational amplifier and summing amplifier 82 drive the data bus 24connected between the scanning unit 12 and the data processing unit 14.

The computer interface circuit 78 is typically a card which plugs intothe expansion bus of data processing unit 14 and primarily comprises A/Dconverters which to convert the analog signals on data bus 24 to digitalvalues on digital output bus 84. The digital output on bus 84 can bestored in temporary and/or permanent memory of the data processing unit14 for subsequent processing.

The operation of the circuit of FIG. 3 can be further understood withreference to FIG. 4, wherein the graph depicts the following function:

    diff=A-B                                                   (equation two)

In equation two, the letter A represents the signal amplitude on line 72(i.e., the magnitude of the signal from photodetector A), and the letterB represents the signal amplitude on line 74 (i.e., the magnitude of thesignal from photodetector B). Therefore, equation two represents theoutput of operational amplifier 80.

For purposes of discussion of the circuit of FIG. 3, it can be assumedthat the reflected beam initially strikes only photodetector A. Furtherfor purposes of simplifying the discussion, it can be assumed thatoperational amplifier 80 has a unity gain. Under these assumptions, thevalue of the function of equation two will equal the magnitude of signalA (i.e., diff=A). Similarly, if the reflected beam strikes onlyphotodetector B, the value of the function will equal the negative ofthe magnitude of signal B (i.e., diff=-B). Both situations are showngraphically in FIG. 4.

In situations where the reflected beam simultaneously strikesphotodetectors A and B, the value of equation two will equal thequantity diff=A-B, where the magnitudes of signals A and B areproportional to the area of the beam spot 86 which strikes thephotodetectors A and B, respectively. Therefore, the output ofoperational amplifier 80 in such circumstances equals the magnitude ofsignal A minus the magnitude of signal B. It should be noted that themagnitude of the amplifier output decreases generally linearly within alinear region L as the beam spot traverses line 70 from photodetector Ato photodetector B.

Referring ,again to FIG. 3, the summing amplifier 82 is used tonormalize the output of differential amplifier 80. More particularly,the output of differential amplifier 80 can be divided by the output ofsumming amplifier 82 to provide the following function, Q:

    Q=(A-B)/(A+B)                                              (equation three)

The operation of division indicated by equation 3 can be implemented byhardware (i.e. by a divider circuit), but is more convenientlyimplemented in software within data processing unit 14. As a result ofsuch a normalization operation, measurements provided by the circuit ofFIG. 3 can be made insensitive to beam intensity, to changes in thereflectivity from the wafer surface, to signal drift, and toenvironmental factors.

For calculations based upon information provided by the circuit of FIG.3, the measurement region of interest is usually only the linear regionL (e.g. ten percent) of the region bounded by lines Z1 and Z2 in FIG. 4.Within that region, the amplitude of the quantity (A-B) changesgenerally linearly with changes in displacement in the z direction. Inpractice, the approximation to linearity is most exact for a limitedrange of values about the point where the signal amplitude functionintersects the z axis.

Utilizing the above-described process provides a very high-resolutiondetermination of the z position of the beam spot. A typical 20 μm beamspot on the detector 32 will permit the detection of a Δz of about 0.005μm, or approximately 10⁻⁸ radian. This resolution corresponds todetecting the diameter of a U.S. quarter dollar from a distance of 1500miles.

This high level of resolution requires that the beam spot fall on therather narrow linear region L(≈0.01 mm) along the z axis of thedetector. If the wafer or other workpiece under test causes a deflectionof the beam which would put the beam spot out of the linear region L,the z-stage 46 can be caused to move to bring the spot back into thelinear region. Under those circumstances, the z position of the beamspot is obtained by utilizing both the z-stage coordinate and thedetector signal. By utilizing the z-stage to effectively extend thelinear region of detector 32, the accurate measurement range of thesystem is greatly expanded.

The operation of the apparatus 10 when it is being used to measure filmstress is illustrated in FIG. 5. In a first step 88, the parameters areentered into the data processing unit 14 such as by keyboard entry.Next, in a step 90, a blank wafer 22 is inserted into the scanning unit12 and placed on pedestal 20. Preferably, the pedestal 20 is providedwith wafer aligning pins (not shown), so the wafer can be replaced onthe pedestal in the same position after processing. The beam detector 32is then calibrated in a step 92. In a step 94, the blank wafer 22 isscanned to provide reference data about its surface topography. Next, instep 96, the blank wafer is removed from the scanning unit 12 and isprocessed to form a thin film over its surface s. Step 98 calls for there-insertion of the processed wafer 22 into the scanning unit 12 andonto the pedestal 20 such that it is aligned with the previous blankwafer position. The beam detector 32 is calibrated again in a step 99for the processed wafer. The processed wafer 22 is then scanned toprovide data concerning the surface topography of the processed wafer ina step 100. The data generated by the steps 94 and 100 is processed in astep 102, and an appropriate output of the processed data is made in astep 104.

If the apparatus 10 is simply used to measure topography of the surfaceof a workpiece, several of the steps of FIG. 5 may be omitted. Forexample, when measuring the curvature of an uncoated hard disk platter,the process would involve steps 88, 90, 92, 94, 102, and 104, where instep 90 the blank wafer is replaced with the disk platter.

FIG. 5a illustrates some of the parameters which may be input as part ofinput step 88. In an input step 106, the number of scans Ns of the waferis entered into the data processing unit 14. In the present embodimentof the invention, Ns is in the range of 1≦Ns≦100. The incremental angleφ of rotation (in degrees) of the pedestal 20 is then calculated byequation one (i.e. φ=360/Ns) in a calculation step 108. The number ofdata points X per scan can be input in a step 110. Alternatively, thenumber of data points X can be set by the system. Other pertinentparameters that could be input as part of input step 88 includes thestress constant of the wafer. The default stress constant for the systemis 3.02×10¹⁸ dynes/cm² ×A/mm for Silicon <100>. If a wafer other thanSilicon <100> is used, the system should be informed in input step 88 sothat the stress constant can be adjusted accordingly. After allappropriate parameters have been input into the data processing unit 14,step 88 is completed as indicated at step 112.

A blank wafer 22 is inserted into scanning unit 12 in step 90 for tworeasons. First, the blank wafer serves as a reflective surface for thelaser beam during the calibrate beam detector step 92. Second, it isdesirable to obtain blank wafer data in step 94 to provide referencedata concerning any curvature in the wafer prior to film deposition.

The calibrate beam detector steps 92 and 99 are illustrated in greaterdetail in FIG. 5b. For these calibration steps, the wafer 22 is held ina stationary position on pedestal 20, and the x stage 56 is immobilized.For calibration purposes, z stage 46 is driven in the z direction bystepper motor 54, thereby causing the beam spot 86 to move across theface of the beam detector 32. As stage 46 is driven in the z direction,its displacement is monitored via stepper motor 54. Then, the value of Qcan be calculated by equation three to provide a measure of the changein value dQ of relative displacements dZ of the stage 46. In otherwords, knowledge of changes in the function Q with discrete z directiondisplacements of stage 46 enables a function dQ/dZ to be calculated. Inessence, this function expresses the slope of the normalized version ofthe graph of FIG. 4 within the limits of the lines Z1 and Z2, and moreparticularly in the linear region L.

In FIG. 5b, the calibration steps 92 and 99 are therefore implemented bysetting a counter Z to zero in a step 114 and then comparing Z with Zmaxin step 116, where Zmax is the maximum number of steps to be taken inthe Z direction. If Z is less than Zmax, Q(z) is calculated, and Z isincremented by one in step 120. The z stage 46 is then moved in the Zdirection by dz, and Z is once again compared to Zmax. Steps 118-122 arerepeated until Z>Zmax. The slope S is calculated by a least square fitof the data points within the linear region L. The step 92 is thencompleted as indicated at 126.

Once the beam detector is calibrated in step 92, data is obtainedconcerning the topography of the blank wafer 22 in a step 94. In FIG.5c, the step 94 includes setting a counter N to zero in a step 128 andcomparing N to the number of scans Ns in a step 130. If N≦Ns, then thecounter X is set to zero in a step 132 and compared to X in a step 134,where X is the number of data points in a scan. If X>X, then BLANK(N,X)is set to the value of Q (equation three) at that point in a step 136.The x stage is then moved by an amount dx in a step 138, and the counterX is incremented by one in a step 140. Steps 136-138 are repeated untilX>X, at which time the wafer 22 is rotated by φ degrees in a step 142.The counter N is then incremented by one in step 144, and steps 130-144are repeated until N is determined to be greater than Ns in step 130, atwhich time step 94 is completed as indicated at 146.

After obtaining the blank wafer data, the wafer 22 is removed from thescanning unit and processed to form a film on the upper surface s. In astep 98, the wafer 22 is then placed back upon pedestal 20 in the sameposition that it was previously as determined by alignment pins (notshown) provided on the pedestal.

The step 100 of obtaining deposited wafer data, is illustrated ingreater detail in FIG. 5d. Step 100 begins with setting counter N tozero in a step 148, and then comparing N to Ns in step 150. If N≦Ns, thecounter X is set to zero in a step 152 and X is compared to X in step154, where X is the number of data points to be taken in a scan of thewafer. The data DEP(N,X) is set to the value of Q (equation three) in astep 156, and the x stage 56 is then moved by dx in a step 158. Thecounter X is then incremented by one in step 160, and X is againcompared with X in step 154. As long as X≦X, steps 156 and 158 arerepeated. When X>X, the wafer 22 is rotated by φ in a step 162, and thecounter N is incremented by one. Steps 150-164 are repeated until N>Ns,at which point step 100 is completed, as indicated at 166.

The next step 102 is to process the BLANK(N,X) and DEP(N,X) data toprovide Ns sets of data relating to the displacement of the deflectedbeam Bd. An example of the processing step 102 is illustrated in FIG.5e. In a first step 168, a set of DIFF(N,X) data is calculated bysubtracting the BLANK(N,X) data from the DEP(N,X) data. The value of thedata DIFF(N,X) for any give N and X is simply DEP(N,X)-BLANK(N,X) forthat given N and X. This operation removes the effect of anypre-existing curvature on the blank wafer 22 so that the curvaturesderived from DIFF(N,X) will be related primarily to the curvaturecreated by the stresses created by the film applied to the wafer. Next,in a step 170, the least mean square (LMS) of the DIFF(N,X) data iscalculated to fit a best fit straight line to the DIFF(N,X) data.Therefore, there will be Ns LMS(N) values if a single straight line isused to approximate the data points of DIFF(N,X) for each scan, whereLMS(N)=mx+b, m being the slope and b being the z axis intersection.Alternatively, a number of LMS approximations of discrete subsets of thedata DIFF(N,X) can be made if the curvature of radius of the surface ofthe wafer varies greatly across a particular scan.

In step 172 the values of LMS(N) are converted to Z displacements by theuse of equation four:

    ZDIFF(N)=LMS(N)/S+c                                        (equation four)

where S was given by equation four and c is a constant. Step 174converts the displacement data to radii of curvature by using equationfive, below:

    R(N)=2Ld{dx/ZDIFF(N)}+c                                    (equation five)

where Ld is the distance traveled by the beam after reflection from thewafer surface 22 (i.e. Br+Bd) and dx is the distance of translation ofthe x stage 56 to create the Z displacement ZDIFF(N). Finally, in a step176, the curvatures related to the multiple scans Ns are aligned to eachother and the step 102 is completed as indicated at 178.

The alignment step 176 is illustrated in greater detail in FIG. 5f.First, in a step 180, the counter N is set to zero. In step 182, areference point P is chosen. Preferably, P is the centerpoint (i.e. theX/2 datapoint) of curve N=0 because this point should be in common withall of the curves. In a decision step 184, the current value of N iscompared with Ns. If N is less than Ns, curve N is aligned with point P,if necessary, in step 186. This step 186 will not be necessary for curveN=0. Next, in step 188, the slope of the tangent to curve N iscalculated. In step 190, the curve N is pivoted around point P until thetangent to the curve is zero. This step is illustrated in FIG. 8 wherethe tangent T0 has an angle β to the z=0 axis. The curve C0 is thenpivoted around P by β degrees until the tangent T0' of curve C0' isequal to zero. The counter N is then incremented by one in a step 191,and steps 186-191 are repeated until N is greater than or equal to Ns,at which time step 176 is terminated as indicated at 192.

FIG. 6 is a graph illustrating some of the data for a single scan N ofthe wafer. In this graph, the horizontal axis is the X axis, and thevertical axis is the Z axis. A first curve 194 represents the dataBLANK(N,X) for a particular scan N and a second curve 196 represents thedata DEP(N,X) for scan N. Curve 198 represents DIFF(N,X) for scan N, andline 200 represents LMS(N). The curve 202 is calculated from the LMS(N)data, and represents the curvature data for the surface of wafer 22taken along a particular scan line N.

In FIG. 7, six curves C0, C1, C2, C3, C4, and C5 (i.e. Ns=6) areillustrated. Each of these curves are separated by the angle φ in thex-y plane. Due to the constant c, the curves are not all perfectlyaligned.

Step 102 of FIG. 5 calls for the processing of the data. This step cantake many forms. For example, the accumulated curvature data can be usedto calculate thin film stress by utilizing algorithms well known tothose skilled in the art. The data processing step 102 can also preparethe data for various forms of graphical output.

Step 104 of FIG. 5 calls for the outputting of data. The stresses alongthe various scan lines as calculated by step 102 can be output inconventional tabular form. Another form of data output is illustrated inFIG. 9. Here, the Ns scans of the wafer have been presented in threedimensional form by providing the curves C(0) . . . C(Ns) to acommercial 3-D rendering program or by utilizing well-known 3-Drendering algorithms. The present invention can therefore be used toprovide three dimensional representations of the topography of a wafersurface.

FIG. 10 illustrates a still further type of output data which can beprovided by step 104. The perimeter 204 is the circumference of wafer 22and the contour lines 206a, 206b, and 206c represent points of equalheight relative to a reference point 208. This "contour mapping" of thesurface of wafer 22 provided yet another way of presenting the curvatureor flatness of the surface s. Algorithms for creating contours are wellknown to those skilled in the art.

While this invention has been described in terms of several preferredembodiments, it is contemplated that alterations, modifications andpermutations thereof will become apparent to those skilled in the artupon a reading of the specification and study of the drawings. It istherefore intended that the following appended claims include all suchalterations, modifications and permutations as fall within the truespirit and scope of the present invention.

What is claimed is:
 1. A method for measuring the topography of asurface comprising:scanning a laser beam linearly across at least aportion of said surface in a first direction; detecting a portion ofsaid laser beam reflected from said surface to develop first scan data;scanning a laser beam across at least a portion of said surface in asecond direction; detecting a portion of said laser beam in said seconddirection reflected from said surface to develop second scan data; andutilizing said first scan data and said second scan data to representthe topography of said surface.
 2. A method for measuring topography asrecited in claim 1 wherein said surface remains substantially stationaryduring said scanning steps and said laser beam is caused to move acrosssaid surface.
 3. A method for measuring topography as recited in claim 1further comprising the step of rotating said surface by an angle priorto scanning said laser beam in said second direction.
 4. A method formeasuring topography as recited in claim 1 further comprising additionalscanning and detecting steps to develop a multiplicity of scan data,where each of said multiplicity of scan data is taken along a differentdirection of said surface.
 5. A method for measuring topography asrecited in claim 4 wherein an angle φ between adjacent scan directionsis given by the equation φ=360/Ns, where Ns is the number of scandirections.
 6. A method for measuring topography as recited in claim 1wherein said first scan data and said second scan data are used tocreate a three-dimensional representation of said surface.
 7. A methodfor measuring topography as recited in claim 1 wherein said first scandata and said second scan data are used to create a two-dimensionalcontour representation of said surface.
 8. A method for measuringtopography as recited in claim 1 wherein said laser beam is scannedusing a beam source, where said method further comprises causingrelative angular motion between said surface and said beam source.
 9. Amethod for measuring topography as recited in claim 1 further comprisingthe step of rotating said surface by an angle prior to scanning saidlaser beam in said second direction.
 10. A method for measuring thetopography of a workpiece surface comprising:scanning a laser beamlinearly across at least a portion of said workpiece surface in a firstdirection; measuring a plurality of positions of a reflected portion ofsaid laser beam corresponding to a plurality of points along said scanof said laser beam in said first direction to develop first scan data;scanning a laser beam linearly across at least a portion of saidworkpiece surface in a second direction; measuring a plurality ofpositions of a reflected portion of said laser beam in said seconddirection to develop second scan data; and using said first scan dataand said second scan data to represent the topography of said workpiecesurface.
 11. A method for measuring topography as recited in claim 10wherein said plurality of positions of said reflected portion of saidlaser beam are measured by detecting displacements of said reflectedportion of said laser beam on a detector as said laser beam is scanned.12. A method for measuring topography as recited in claim 10 whereinsaid first scan data and said second scan data describe changes inheight along said scanned portions of said workpiece surface.
 13. Amethod for measuring topography as recited in claim 10 wherein saidworkpiece surface remains substantially stationary during said scanningsteps and said laser beam is caused to move across said workpiecesurface.
 14. A method for measuring topography as recited in claim 10further comprising additional scanning and detecting steps to develop amultiplicity of scan data, where each of said multiplicity of scan datais taken along a different direction of said workpiece surface.
 15. Amethod for measuring the topography of a workpiece surface comprisingthe steps of:(a) directing a laser beam onto said workpiece surface; (b)detecting a portion of said laser beam reflected from said workpiecesurface to obtain a datapoint; (c) scanning said laser beam across saidportion of said workpiece surface by a predetermined distance in a firstdirection; (d) repeating steps (b) and (c) until a number of saiddatapoints have been obtained, thereby developing first scan data; (e)repeating steps (a) through (d) in a second direction on said workpiecesurface to develop second scan data; (f) utilizing said first scan dataand said second scan data to determine a topography of said workpiecesurface.
 16. A method for measuring topography as recited in claim 15wherein said step (d) includes repeating steps (b) and (c) until apredetermined number of datapoints have been obtained.
 17. A method formeasuring topography as recited in claim 15 further comprising causingrelative angular motion between said film surface and a beam source thatdirects said laser beam.
 18. A method for measuring topography asrecited in claim 17 wherein said causing said relative angular motionincludes rotating said workpiece surface by an angle.
 19. A method formeasuring topography as recited in claim 15 further comprising repeatingsteps (a) through (d) in a plurality of additional different directionsto develop a multiplicity of scan data.